Global boundedness of solutions in a reaction–diffusion system of Beddington–DeAngelis-type predator–prey model with nonlinear prey-taxis and random diffusion

In this paper, a reaction–diffusion system of a predator–prey model with Beddington–DeAngelis functional response is considered. This model describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which leads to the collection of u). We use some approaches to prove the global existence-boundedness of classical solutions and overcome the substantial difficulty of the existence of a nonlinear prey-taxis term.